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Experimental observations of extensive air showers have revealed an excess ofthe muon content with respect to their theoretical simulations, which we referto as the muon puzzle. This muon puzzle hampers a precise determination of theultra-high-energy cosmic ray mass composition. We investigate the potential ofproducing states of dense quark-gluon matter (which we call fireballs) toresolve the muon puzzle as quantified with data from the Pierre AugerObservatory on the depth of the shower maximum and the number of muons atground. Adopting a phenomenological fireball model, we find that theinelasticity enhancement associated with the formation of a plasma state is intension with data on the electromagnetic longitudinal shower development.Instead, we restrict the fireball model to only enhance the strangenessproduced in Standard Model hadronic interactions, and dub this model thestrangeball model. With an analytic approach based on the Heitler-Matthewsmodel we then find explicit sets of strangeball parameters that resolve themuon puzzle. Constraints from data on shower-to-shower fluctuations of the muonnumber require strangeness enhancements already at energies accessible tocurrent-generation collider experiments. At Tevatron and LHC energies weestimate 40% of the interactions to produce strangeballs, corresponding to a5-9% increase of the average fraction of energy retained in the hadroniccascade compared to predictions from current hadronic interaction models. Acomparison with relevant measurements of the LHCf and LHCb detectors does notdirectly exclude this scenario, though the obtained tension with LHCb suggestsa stringent test at 14 TeV.

Modeling Strangeness Enhancements to resolve the Muon Excess in Cosmic Ray Extensive Air Shower Data